Orienting Parts With Shape Variation

We study the problem of orienting a part with given admitted shape variations by means of pushing with a single frictionless jaw. We use a very general model for shape variations that is defined by two given convex polygons PI ⊆ PE. In this model, any valid instance must contain PI while it must be contained in PE. The problem that we solve is to determine, for a given h, the sequence of h push actions that puts all valid instances of a part with given shape variation into the smallest possible interval of final orientations. The resulting algorithm runs in O(hn) time, where n=|PI|+|PE|.